

A173280


First column of the matrix power A173279(.,.)^j in the limit j>infinity.


3



1, 1, 3, 7, 29, 129, 757, 5185, 41155, 368351, 3671635, 40295943, 482758111, 6268066531, 87668492115, 1314023850727, 21011431917453, 357014074280785, 6423561495057421, 122004755658629081, 2439367774898883497, 51213663674167659301, 1126452985959434543237
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OFFSET

0,3


COMMENTS

We can generalize A173279 to other matrices derived from some sequence S by Smat(n,k) := S(nr*k), r >=2,
and find that they define sequences B(x) via S(x)= B(X)/B(x^r), b(n) = sum_{t=0..n, nt =0 (mod r)} S(t)*B_{(nt)/r} .
This here is the case of S=A000142 and r=2.


LINKS

Table of n, a(n) for n=0..22.


FORMULA

A000142(x) = A(x)/A(x^2), where A(x) and A000142(x) are the o.g.f.'s associated with A000142 and this sequence here.
sum_{n>=0} 1/a(n) = 2.519966353393413186683398448854995831308...
a(n) = (A173279^j)(n,0).
a(n) = sum_{t=0..n, nt even} t!*a_{(nt)/2}. [R. J. Mathar, Feb 22 2010]


MAPLE

A173280 := proc(n) option remember; local a, l; if n = 0 then 1; else a :=0 ; for l from n to 0 by 2 do a := a+ l!*procname((nl)/2) : end do ; a ; end if; end proc:
seq(A173280(n), n=0..60) ; # R. J. Mathar, Feb 22 2010


CROSSREFS

Cf. A000142
Sequence in context: A110613 A088095 A217576 * A141477 A211371 A302157
Adjacent sequences: A173277 A173278 A173279 * A173281 A173282 A173283


KEYWORD

nonn


AUTHOR

Gary W. Adamson, Feb 14 2010


EXTENSIONS

Extended by R. J. Mathar, removed invalid comment on convergence to e. Feb 22 2010
Corrected index of B in the convolution formula in the comment  R. J. Mathar, Mar 23 2010


STATUS

approved



